Large scale mathematical modeling often requires derivatives, for example, for the optimization of objective functions, resolution of nonlinear systems, and the analysis of sensitivities between input and outputs. The model may be based on one or more mathematical formulas and employ a simple linear equation, a complex neural network, mapped out by sophisticated software, or other implementation.
Agents may desire to break up these mathematical models into component portions so that they can be reused in multiple models. Furthermore, agents desire to keep these component portions proprietary. Difficulties may arise where derivatives of functions contained within the models are needed at or before compile-time but secrecy of the functions must be maintained.